I checked the website suzie referenced. Apparently there is availability at the Ahwahnee, Wawona, and Tenaya - all are fine hotels. I've stayed at the Wawona and found it to be a charming historic hotel, although the drive into the valley takes almost an hour.
Consider that low clouds will obscure the views. Snow is fun and it keeps the less intrepid travelers away from Yosemite. Lake Tahoe has more things to do - gambling, dining and skiing (Squaw Valley is open w/ a 31" base) - in rainy/snowy weather. Otherwise, If you have a chance to come another time, go when the weather will be more predictable. Go where you won't feel bad that you spent good money just to get rained on. Go where there is something else to look at besides nature.
As far as getting caught out in the middle of nowhere in the rain or snow while hiking... well... Bring your rain gear, warm clothes, and wear good shoes. Don't plan long hikes. Storms, except for the typical Sierra thundershower, don't occur suddenly. Weather forecasts are usually accurate for the next day. A cold, windy, forebodingly cloudy, drizzly, or full-on rainy or snowy morning will cause you to cancel your hike.